Flexure Performance of Externally Bonded CFRP Plates-Strengthened Reinforced Concrete Members

(is paper investigates the flexural behavior of CFRP plate-strengthened concrete structures. Specimens of the CFRP platereinforced beam were designed and tested by the four-point flexural test. (e load-deflection relationship, failure modes, and crack propagation were analyzed. (e results showed that the postcracking stiffness and bearing capacity of the test beams can be improved by the additional anchoring measures for CFRP strengthening. (e relationship between flexural moment and curvature was analyzed by introducing a MATLAB program. (e calculation model between curvature, flexural moment, and stiffness was derived for the CFRP plate-strengthened structure. (e recommended calculation model was applied in the analysis of deflection, and the theoretical values were compared with the test results.


Introduction
e carbon fiber-reinforced polymer (CFRP) has advantages of lightweight and high strength [1]. Considering its durability and easy construction compared with other traditional strengthened materials, CFRP has been applied in strengthening and repair of damaged reinforcement concrete structures [2,3]. e advantages of CFRP-strengthened structure have been studied in static and dynamic methods [4,5]. Several series of double shear specimen have been tested and analyzed to study the interfacial behavior between CFRP and concrete. e test and analysis results show that the crack growth rate increases with the increase in the stress level, and a calculation model was proposed to describe the change law between the crack growth rate and the stress level [6]. Numerical and theoretical investigations were conducted on a CFRP-strengthened cracked steel plate by considering the stress intensity factors, and numerical results and theoretical results were compared to validate the proposed expressions [7]. In addition, the bond behavior of FRP-concrete interface under sustained loading was studied for reliability analysis, and the CFRP-concrete fracture energy of the bond behavior was directly obtained by the measured local bond-slip curves. Numerical tests were also performed on prestressed FRP-bonded beams based on a nonlinear model to gain the short-term behavior of prestressed CFRP-concrete beams [8].
In recent years, the CFRP reinforcement method is also increasingly used for strengthening the concrete bridges [9][10][11]. e numerical analysis of 3D nonlinear finite element method was carried out on the girder bridge with CFRP-strengthened RC beams, and the distributions of load deflection and the concrete-CFRP plate had been investigated [9]. ese results show that the new Truss-link interface elements can be effectively adopted for modelling the FRP-strengthened RC structural component. A new type of bridge deck composed of innovative pultruded fiber-reinforced polymer composite sandwich panels was proposed [10]. Based on the first-order shear deformation theory, the failure mode, flexural capacity, and other aspects of bridge decks under different working conditions were researched with four-point flexural tests.
CFRP can effectively extend the ductility and bearing capacity of the concrete structures [11][12][13]. Seismic behavior of gravity railway bridge pier strengthened with CFRP was studied [14]. It was found that the load-carrying capacity of the bridge pier can be enhanced by the CFRP wrapping method, and this strengthening method can be applied to improve the vulnerability of gravity bridge pier at the pierfooting region. CFRP-strengthened RC beams were experimentally studied and analyzed under sustaining load [15]. eir research results indicated that the load magnitude during CFRP reinforcement process is an important indicator of the ultimate strength of reinforced concrete beams, while the ultimate strength of CFRP-strengthened concrete beams is basically the same even with small initial load. Experimental and analytical investigations were also carried out on the CFRP shear and flexural strengthened concrete beams [16,17]. e experimental data indicated that greater thicknesses of CFRP did not increase the shear capacity of specimens with no unanchored method, compared with both control and unanchored CFRP-strengthened beams. It can be concluded that the CFRP anchorage method did lead to moderate increases in shear capacity. e main failure mode of CFRP-reinforced members is generally due to the stiffness characteristic concentration near the interface of CFRP and concrete. erefore, accurate prediction of postcracking stiffness is important for preventing the occurrence of debonding failure [18][19][20][21]. e test results show that CFRP-strengthened concrete structure can improve the strength and stiffness performance of the structure, and the lateral offset of CFRP from the longitudinal centerline has little effect on the flexural behavior of the concrete-CFRP interface [22]. When the crack width is small, the crack has a certain enhancement effect on the bonding behavior of CFRP-strengthened concrete structure in the initial stage. e crack development at this stage has little effect on the load-deflection curve of CFRP-reinforced concrete structures. When the crack width is large, the bond slippage phenomenon will be increased with the development of concrete cracking. A hybrid system composed of CFRP and reinforced steel was proposed to improve the strength and ductility of CFRP-reinforced concrete structures [23]. e results show that the hybrid reinforcement ratio between CFRP and steel will affect the balance between strength and ductility in flexural design which will affect the flexural performance of hybrid beam, while better strength and ductility of the hybrid beam can be obtained with reasonable mixing and strengthening ratio between FRP and steel. Yuan et al. [24,25] investigated the crack and mechanical behaviors of CFRP plate-reinforced bridge roofs under high temperature with different anchoring measures. It is shown that the average crack spacing is more effectively reduced by the additional anchoring measures placed at the midspan and the support position.
is paper investigates the flexural behavior of CFRP plate-strengthened concrete structure. CFRP platestrengthened concrete test beams were designed and constructed according to the structural analysis of the box girder. Four-point flexural tests were carried out on the specimens. e crack propagation, flexural moment-curvature relationship, deflection, and failure modes were investigated.
e stiffness variation and the debonding mechanism of the test beams were comparatively studied. A theoretical calculation model was derived for the CFRP plate-strengthened structure by introducing MATLAB program. An accurate calculation of the relationship between flexural moment and curvature of the CFRP platestrengthened concrete flexural members was proposed as well. e theoretical model was applied in the deflection analysis of flexural beam. e relationship between flexural moment and stiffness can better predict the deflection of CFRP-strengthened concrete structure by comparing the theoretical calculation results with experimental results.

Bridge Diseases and Reinforcement Scheme
Under the coupling effect of vehicle load and a hot humid environment in South Asia, cracks appeared in the box girder roof of the Bangabandhu bridge. e cracks can be divided into several types according to the crack location, cracking reason, and direction. e maximum crack width can reach 6.4 mm. Some representative crack shapes and their locations are presented in Figure 1.
Carbon fiber-reinforced polymer (CFRP) is a lightweight composite material with ultrahigh tensile performance. It is also often used to strengthen structures in civil engineering. In this project, CFRP plates were also adopted to strengthen the roof of box girder, and its main working position was in the tensile side of the negative moment zone. CFRP plates were horizontally pasted on the bridge roof to delay the development of longitudinal cracks in the bridge. e reinforcement scheme of bridge roof using the CFRP plate is shown in Figure 2

Specimen Design.
Based on the load distribution on the Bangabandhu bridge, the negative moment zone in the range of 2000 mm on both sides of the box girder web was selected to study. Force analysis result of the box girder is shown in Figure 3. e CFRP plate-strengthened specimens were designed according to the principle of action equivalence. e specimen is a concrete slab beam with a rectangular cross section. e length of the specimen is 4.00 m, and the cross-sectional size is 0.65 m in width and 0.28 m in height.
e specimen adopted in this study is shown in Figure 3. According to the structural form of the selected segment of box girder roof, the upper surface of the concrete slab beam specimen was taken as the tension side and the lower surface was taken as the compression side. e concrete adopted in this test was grade C40, and the thickness of concrete cover is 34 mm. e grade of rebar was HRB 400, seven tensile steel bars and seven compressed steel bars were arranged in the specimens, and the reinforcement ratio was 0.87%. ree pieces of CFRP plates were pasted on the upper surface of the specimen. e CFRP plate was 3 400 mm in length and 100 mm in width, and its thickness was 1.4 mm. e interval of each CFRP plate was 250 mm. In order to simulate the high-temperature action of asphalt paving construction, the asphalt layer was also paved on the surface of the specimen after the CFRP plates were curded. e specimen with asphalt layer is presented in Figure 3.
One control specimen and three CFRP-strengthened specimens were prepared in this test. e classification of the specimens is listed in Table 1. e control specimen FDBL is a concrete slab beam without strengthened measure and additional anchorage measure. e specimens TM-1 to TM-3 were strengthened with CFRP plates as shown in Figure 4(a). Strain gauges were also arranged on the CFRP plate, and the arrangement scheme of strain gauges is presented in Figure 4(a). Considering the asphalt layer paved on the surface of the specimen, part of the asphalt layer was removed before placing the stain gauges. e CFRP plate-strengthened specimens with asphalt layer partly removed is presented in Figure 4(a). Additional anchorage measure by horizontally pasting a steel plate on the CFRP plates was adopted to delay the debonding failure occurring in the CFRP-strengthened specimens. e form of the additional anchorage measure is shown in Figure 4

Specimen Preparation
(1) Concrete Pouring Process. After the reinforced skeleton frame of the specimens was tied, the strain gauges were attached to the upper and lower sides of steel bars at the midspan of the specimen. e pouring process is shown in Figure 5.
(2) CFRP Strengthening Process. Firstly, the surface of the CFRP plate is roughened to remove the surface demould wax.
Secondly, the deteriorated layer on the concrete surface was removed with a wire-wheel angle grinder. e surface is cleaned to make it neat and solid. e cement is used to level the surface of the specimen. Before pasting the CFRP plate, the ink line should be prepared to ensure correct positions of the CFRP plate. e surface preparation of the specimen is shown in Figure 6. Finally, after the CFRP plate is pasted, it is cured by bolting with wood strips. e specific method is as follows: two bolts are placed on both sides of the CFRP plate at intervals of 50 cm, and a vertical long wooden strip is first pressed on the surface of the CFRP plate. en, the surface of the vertical long wooden strip is pressed with a horizontal short wooden strip. ey are pressed evenly together and are fixed on the surface of the carbon plate. e wooden strips are removed after 3 to 7 days of curing.
(3) Asphalt Paving Construction. Considering that the roof of the box girder was paved with asphalt layer after strengthening with CFRP plates, it is necessary to simulate the high temperature conditions of the real construction process. After curing the CFRP plates, an epoxy mortar insulation layer was set according to the pavement scheme ( Figure 2). After curing is completed, the asphalt is paved and rolled with heavy equipment. e asphalt paving process is shown in Figure 7.

Material Performance Test
. Performance of materials was tested according to the corresponding standard code, and the tested results of material performance are shown in Table 2   End position and midspan position TM-3 End position and bearing position specimens were tested as well, and their material performances were also obtained.

Test Setup.
According to the structure form of the box girder roof and traffic distribution, two supports were arranged near the midspan position of the specimen. Two 30 t hydraulic jacks were adopted in this test, and they were arranged on both ends of the specimen to simulate the traffic loads on the box girder. e shear span of specimen is 1400 mm. e test setup is presented in Figure 3. A preload of 5 kN was applied firstly, and then, an increasing load of 20 kN per stage was loaded on the specimen. e loading pattern of the specimen is shown in Figure 8. Loading was stopped when any of the phenomena of concrete crushing, yield of steel bar, or debonding failure of CFRP plate were observed.

Load-Displacement Relationship.
Load-displacement relationship of the control specimen and the strengthened specimens were compared. Different relationships of specimens in this test are shown in Figure 9. It can be seen from Figure 9 that the curves of strengthened specimens were basically same. erefore, it can be concluded that additional anchoring measures at different positions have little effect on the bearing capacity of the CFRP-strengthened specimens. In addition, the curves of control specimen and strengthened specimen were similar in the initial stage. During this stage, the loading level was small and each specimen was in the elastic stage, and the tensile force in the specimen was mostly shared by the concrete and steel bars.
For the control specimen, the concrete in the tensile zone was out of work after the first crack occurred in the pure flexural section, and the tensile force was taken away by the steel bar. While for the CFRP-strengthened specimens, the tensile force was shared by the CFRP plates and steel bars after the concrete was out of work. Due to the application of CFRP plates, the raising rate of neutral axis was delayed.   Debonding failure of the surface concrete and CFRP plate, concrete crushing, and other failure modes can be observed in the CFRP-strengthened specimens as shown in Figure 10. It can be seen from Figure 10 that CFRP-concrete interfacial debonding failure of the CFRP-strengthened specimens was mainly caused by the flexural shear crack. e debonding failure mainly occurs in the thin layer of concrete below the adhesive layer. During the test, cracks began to appear in the constant moment zone and then gradually extended toward both sides.
e CFRP plate at the end position debonded off firstly. Longitudinal slip of CFRP plates occurred at the end of specimen. e CFRP plate in the constant moment zone debonded off from the concrete surface simultaneously.

Crack Propagation Morphology.
After the loading procedure has completed, cracks of specimen were observed. It was found that the crack distribution is mainly concentrated on both sides of the support, including the constant moment zone and at the range of 400 mm on both sides of the bearing. us, the cracking in this range was presented. e crack development patterns of specimen are presented in Figure 11. e main flexural crack perpendicular to the concrete tensile side occurred in the initial stage of crack formation. e root crack near the steel bar position appeared at the moment when the specimen approached failure.
As can be seen from Figure 5, the cracking space and height of the specimen were larger than those of the specimen strengthened by the CFRP plate, because the control specimen was not strengthened by the CFRP plate. e bonding shear stress between the interface of CFRP plate and concrete can effectively control the expansion of cracks in the concrete tensile zone. e statistics of crack distribution in the constant moment zone are shown in Table 3.
For the ratio of the maximum crack spacing to the average crack spacing and the ratio of the maximum crack spacing to the minimum crack spacing, it can be seen from the Table 3 that ratio of the control specimen is much smaller than that of the strengthened specimen, while the maximum cracking height of control specimen is higher than that of CFRP plate-strengthened specimens. It can be concluded from Table 3 that the CFRP plate-strengthening method can effectively delay the cracking process of concrete structure.

Theoretical Investigation for Relationship of Stiffness and Curvature
e CFRP plate-reinforced concrete structure was taken as the research object. e following basic assumptions were used in this study. Firstly, the specimen follows the plane section assumption, i.e., the section deformation should be a plane. Secondly, the CFRP plate is assumed as a linear elastic material. e stress-strain relationship of the steel bar is considered to be linear before it reaches the yield strength, and when it reaches the yielding strength, its stress is considered as a constant. However, for the concrete material, the concrete is considered to be cracked when it reached its tensile strength, and the concrete stress at the cracked place dropped to zero.

eoretical Calculation Model.
Section strain and stress distribution of the specimen are presented in Figure 12. e cross section of the CFRP plate-strengthened concrete specimen can be divided into finite strips. e stress in each strip is assumed to be evenly distributed, and the stress value is equal to the stress value at the center of its strip section. e strain distribution characteristics in Figure 12 can be calculated with the following formula: e following equation can be obtained from Figure 7 by the force balance relationship: e following equation can also be obtained from where n is the number of strips divided in the concrete section. σ ti is the concrete tensile stress at the center of the i th layer of the concrete tension zone, and σ ci is the concrete compressive stress at the center of the i th layer of the concrete compression zone. b is the sample section width. e flexural moment-curvature relationship of the CFRP plate-strengthened concrete structure was realized by the MATLAB programming method as recommended in the previous study [24]. e specific calculation steps are shown as follows: (1) An initial value is given to the compressive strain ε c of the concrete compression side.  e corresponding calculation process is shown in Figure 13.

Relationship between Curvature and Moment.
Taking the specimens FDBL and TM-1 as examples, the exural momentstrain relationship of the two specimens is shown in Figure 14.
According to the relationship between the strain and exural moment obtained from the experimental test (Figure 14), the relationship between section curvature and exural moment can be calculated by the MATLAB program presented in Figure 13. e comparison of theoretical results and experimental results is shown in Figure 15.
It can be seen from Figure 15 that the calculated cracking moment is much smaller than the test results, and the experimental result and the calculated value of the ultimate exural moment are not much di erent. is is mainly because the e ect of the asphalt layer on the tension side was not considered when calculating the cracking moment. In addition, because the debonding failure between FRP and concrete was not considered in the MATLAB program, the calculation result of the ultimate exural moment of the CFRP-reinforced test piece (such as specimen TM-1) is larger than the test result.
In addition, the exural main crack in the pure exural section of the specimen will expand with the increasing load, and the CFRP plate will debond from the concrete surface. After the debonding failure of the CFRP plate, loads will no longer be added on the specimen. is is the reason for the short curve length of the test result after the yield of steel bar as shown in Figure 15.

Relationship between Moment and Sti ness.
e average curvature of the section can be calculated based on the at section assumption, and the formula is shown as follows: where c m is the average curvature radius of the section, B s is the section stiffness under short-term load, ε sm is the average strain of the tensile steel bar, and ε cm ′ is the average strain of the concrete at the edge of the compression area. e section flexural moment can be obtained according to the calculation model shown in Figure 16, and the formula is shown in the following equation: where η s and η f are the internal lever arm coefficient of the steel bar and the CFRP plate, respectively. us, the average strain of the tensile steel bar can be obtained as follows: It can be seen from Figure 13 that the concrete stress in the compression zone adopts a curve distribution. erefore, a coe cient ω is introduced when calculating the concrete stress at the edge of the compression zone σ c ′ . us, the resultant force of the concrete in the compression zone can be calculated by the following formula: where c f ′ is the ratio of the compressed ange area to the effective area of the web in the T-beam section and ξ is the height coe cient of the compression zone at the cracking section.
Considering the force of the concrete in the compression zone and the force in the CFRP plate to the combined point of the tensile reinforcement, the exural moment can be calculated as follows: where υ c is the elastic characteristic coe cient of concrete. By introducing the nonuniform coe cient of concrete strain in compression zone ψ c ′ , the mean value of the concrete strain can be obtained as follows: Assuming that ς is the comprehensive coe cient of the average strain of the concrete in the compression zone, then ς can be expressed as follows: us, equation (9) can be converted into the following formula: e comprehensive coe cient of the average strain of the concrete in the compression zone ς can be calculated by MATLAB, and the calculation results are presented in Figure 17.
It can be seen from Figure 17 that the comprehensive coe cient of the average strain ς decreases with the increase of the section exural moment. It decreases rapidly after the occurrence of the crack, while it is basically unchanged before the yield of steel bar. erefore, the calculation of the comprehensive coe cient can ignore the e ect of loads before the steel bar yields. e value at the yield point of the steel bar is taken as the numerical t point of the comprehensive coe cient in this study.
By tting the test results in this test, the relationship between α Es ρ s /ς and α Es ρ s can be obtained as shown in Figure 18, and the corresponding formula is shown as follows: α Es ρ s ς 9.70078α Es ρ s − 0.04895.
us, the following formula can be derived by the above analysis: where α Es E s /E c , ρ s A s /bh 0 , (ε f /ε s ) 1.9(h/h 0 ) − 1, η s 0.87, and η f h f 0.87h 0 + a f . ψ s is the nonuniform coe cient of steel bar. erefore, the short-term sti ness before the yield of steel bar can be expressed as follows: However, the contribution of the longitude steel bar to the section sti ness is small after the yield of the steel bar, and the CFRP plates are still in the state of linear elasticity at this time.
erefore, the strain of CFRP plate should be adopted when calculating the section curvature and sti ness. e average curvature of the section after the yield of steel bar can be expressed as follows: And the section flexural moment can be expressed as follows: e average strain of the CFRP plate can be presented as follows: e section flexural moment can be expressed by using the following equation: e concrete strain in compression zone can be obtained as follows: Applying the same method, the short-term stiffness formula after the steel bar yields can be derived as follows:

Application in Deflection Analysis.
e maximum deflection of the specimen under concentrated load can be obtained according to formula (20): where l is the span of beam, a is the distance between the loading point and the support, and B is the section stiffness which can be obtained by using the equations (14) and (20). e comparison of deflection between the theoretical value calculated, simulation results in the previous study [25], and experimental values is shown in Figure 19.
It can be seen from Figure 19 that the theoretical calculation result and the finite element simulation result of the deflection-flexural moment agree well with the experimental results. e relationship between stiffness and curvature derived by the MATLAB program recommended in this paper can better predict the deflection analysis of CFRP plate-strengthened concrete structures.

Conclusion
is paper investigates the flexure performance of externally bonded CFRP plates-strengthened reinforced concrete members. Specimens of the CFRP plate-strengthened beam were designed and tested. e crack propagation, momentcurvature relationship, and debonding failure modes were analyzed. e relationship of stiffness-curvature was theoretically investigated by adopting a MATLAB program. e following conclusions can be drawn: (1) e CFRP plate has a good inhibitory effect on the cracking expansion. Different positions of additional anchorage measure did little effect on the postcracking stiffness. (2) e yield flexural moment and the ultimate flexural moment value of the CFRP plate-strengthened test specimen are larger than those of the no-strengthened specimen. (3) e analysis of relationship between flexural moment and curvature for the CFRP plate-reinforced concrete flexural members can be realized by the MATLAB programming method adopted in this paper. e deflection of specimens can be predicted by applying the relationship of moment-curvature concluded in this paper.
Data Availability e figure and table data used to support the findings of this study are included within the article.